Categorical Torelli theorem for Gushel-Mukai threefold
[Math. Dept.]
March 22, 2021 10:00-12:00
W303 School of Mathematics
SPEAKER
Shizhuo Zhang (University of Edinburgh)
ABSTRACT
A conjecture of Kuznetsov-Perry states that the equivalence of the Kuznetsov components of ordinary Gushel-Mukai threefolds implies they are birational. We show that the Bridgeland moduli space of -1 class stable objects in the Kuznetsov components is either minimal model of Fano surface of conics or the moduli space of semistable torsion free sheaves MG(2,1,5). As a result, we prove the Kuznetsov-Perry's conjecture for general Gushel-Mukai threefolds. This is a joint work with Augustinas Jacovskis and Xun Lin. If time permits, I will talk about the Brill-Noether locus of Bridgeland moduli space in the Kuznetsov components and its application to the refined categorical Torelli for all index 1 prime Fano threefolds, joint work with Augustinas Jacovskis.
SUPPORTED BY
School of Mathematics, Sichuan University